Question

cho b mũ 2=ac chứng minh rằng

a mũ 2 +b mũ 2 phần b mũ 2 + c mũ 2 =ac

 

Answer 1

\(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a^2+ac}{ac+c^2}=\dfrac{a\left(a+c\right)}{c\left(a+c\right)}=\dfrac{a}{c}\)

Answer 2

Ta có \(b^2=ac\Rightarrow\dfrac{a}{b}=\dfrac{b}{c}\)

\(\Rightarrow\left(\dfrac{a}{b}\right)^2=\left(\dfrac{b}{c}\right)^2=\dfrac{a}{b}.\dfrac{b}{c}=\dfrac{a^2}{b^2}=\dfrac{b^2}{c^2}\)

\(\Rightarrow\dfrac{a}{c}=\dfrac{a^2}{b^2}=\dfrac{b^2}{c^2}=\dfrac{a^2+b^2}{b^2+c^2}\)

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